Problem: Simplify the following expression: $ y = \dfrac{-2t - 8}{6} - \dfrac{-9}{2} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-2t - 8}{6} \times \dfrac{2}{2} = \dfrac{-4t - 16}{12} $ Multiply the second expression by $\dfrac{6}{6}$ $ \dfrac{-9}{2} \times \dfrac{6}{6} = \dfrac{-54}{12} $ Therefore $ y = \dfrac{-4t - 16}{12} - \dfrac{-54}{12} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{-4t - 16 + 54 }{12} $ Distribute the negative sign: $y = \dfrac{-4t - 16 + 54}{12}$ $y = \dfrac{-4t + 38}{12}$ Simplify the expression by dividing the numerator and denominator by 2: $y = \dfrac{-2t + 19}{6}$